In this talk we consider real analytic functions, i.e. functions which can be described locally as convergent power series and ask the following: Which real analytic functions definable in $\mathbb{R}_{\textnormal{an,exp}}$ have a holomorphic extension which is again definable in $\mathbb{R}_{\textnormal{an,exp}}$? Finding a holomorphic extension is of course not difficult simply by power series expansion. The difficulty is to construct it in a definably way.

The talk is organized as follows: At first the notion of definable complexification will be defined and some existing results will be presented. We will not answer the question above completely, but we will introduce a large non trivial class of definable functions in $\mathbb{R}_{\textnormal{an,exp}}$ where for example functions which are iterated compositions from either side of globally subanalytic functions and the global logarithm are contained and give results for definable complexification for this class.

Bio: Andre Opris is a German mathematician. He will earn his doctoral degree in March this year. Then he will work as a postdoctoral fellow at the Chair of Algorithms for Intelligent Systems at the University of Passau. At the moment his research is about holomorphic extensions of real analytic functions in o-minimal structures.